SUM THEOREMS FOR MAXIMALLY MONOTONE OPERATORS OF TYPE (FPV)

被引：4

作者：

Borwein, Jonathan M. ^{[1
]}

Yao, Liangjin ^{[1
]}

机构：

[1] Univ Newcastle, CARMA, Newcastle, NSW 2308, Australia

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2014年 / 97卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

constraint qualification; convex function; convex set; Fitzpatrick function; linear relation; maximally monotone operator; monotone operator; operator of type (FPV); sum problem; LINEAR RELATION; CONVEX-SETS; DOMAIN;

D O I：

10.1017/S1446788714000056

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The most important open problem in monotone operator theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar's constraint qualification holds. In this paper, we establish the maximal monotonicity of A + B provided that A and B are maximally monotone operators such that star(dom A) boolean AND int dom B not equal phi, and A is of type (FPV). We show that when also dom A is convex, the sum operator A + B is also of type (FPV). Our result generalizes and unifies several recent sum theorems.

引用

页码：1 / 26

页数：26

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